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BHOoi
BHOoi16-Pearl
16-Pearl
Oct 7, 2016 5:47 AM UTC
Question

How to create evenly distributed points on a sphere?

A very simple problem but i failed to figure it out.

Is there an easy way to create the points? Any suggestions/tricks? Thanks

    29 replies

    TobiasLarsson12-Amethyst
    12-Amethyst
    Oct 7, 2016 7:32 AM UTC

    Could this help?

    Reg: creating a pattern in sphere

    Help in golf ball modelling

    GOLF - Gentleman Only, Ladies Forbidden?

    //Tobias

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    BHOoi
    BHOoi16-PearlAuthor
    16-Pearl
    Oct 7, 2016 8:07 AM UTC

    wow, none looks simple and some are not evenly spaced. Good reference anyway, thanks. Those were about 3 years ago, hopefully Creo is more capable now

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    dschenken2-Explorer
    2-Explorer
    Oct 8, 2016 12:14 AM UTC

    I searched Google for "points evenly spaced on sphere" and got this: Distributing points on the sphere | School of Mathematics and Statistics which mentions "it is not possible to equally distribute points on the sphere except in a few special cases"

    It's a difficult problem for anything not trivial. It does not surprise me that Creo does not address this.

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    BHOoi
    BHOoi16-PearlAuthor
    16-Pearl
    Oct 10, 2016 12:47 AM UTC

    I have tried patterning but it's still pretty manual. I don't have any image, and just thought of creating something similar to a golf ball.

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    BHOoi
    BHOoi16-PearlAuthor
    16-Pearl
    Oct 10, 2016 1:16 AM UTC

    I got this link from PTC's reply, but still have no clue how to creat it

    https://support.ptc.com/appserver/cs/view/solution.jsp?n=CS177218&lang=en_US

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    Patriot_1776
    Patriot_177622-Sapphire II
    22-Sapphire II
    Oct 11, 2016 1:52 PM UTC

    Pshaw, that's easy.....I just put one point at the North pole, and one at the South pole (2 "points" total), exactly per your request, done! 

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      BHOoi
      BHOoi16-PearlAuthor
      16-Pearl
      Oct 12, 2016 3:02 AM UTC

      Capture.JPG

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      BHOoi
      BHOoi16-PearlAuthor
      16-Pearl
      Oct 12, 2016 3:12 AM UTC

      I found a page below:

      How can I generate uniformly spaced points on the surface of a sphere? - Quora

      and i ended up with:

      Capture.JPG

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        Patriot_1776
        Patriot_177622-Sapphire II
        22-Sapphire II
        Oct 13, 2016 1:11 PM UTC

        Actually, I never got to play around with making a golf ball, but, this is exactly what I was thinking I would try.  Since a sphere can be divided up into equal triangular facets, I figured an approach like this would work.  Nice find!

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        HarikrishnanR1-Visitor
        1-Visitor
        Oct 12, 2016 7:08 AM UTC

        GOLF - Gentleman Only, Ladies Forbidden? - PTC Community-  Vladimir Palffy

        -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

        Thanks

        Hari

        “Share your knowledge. It is a way to achieve immortality.” - Dalai Lama.

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        BHOoi
        BHOoi16-PearlAuthor
        16-Pearl
        Oct 14, 2016 2:41 AM UTC

        This is how I construted the edges of the trinagle of regular icosahedron.

        Capture.JPG

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        BHOoi
        BHOoi16-PearlAuthor
        16-Pearl
        Oct 14, 2016 2:55 AM UTC

        another approach:

        Capture.JPG

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        Kevin1-Visitor
        1-Visitor
        Oct 14, 2016 3:23 PM UTC

        Wiki has info that talks point distances relate to the radius of a sphere. The simplest approach for the icosahedron that I found is to create a sketch with the diameter desired, create a line that goes through the center with the ends on the circle, place points on each end of the line since the points will alternate from northern to southern hemisphere, write a relation for the angle of the line from the latitudinal plane of arctan(.5), pattern the sketch about the longitudinal axis with a spacing of 5 element within 360 degrees, and the final two points are at the north and south poles of the sphere.

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        TomD.inPDX17-Peridot
        17-Peridot
        Oct 15, 2016 11:55 PM UTC

        Have you tried the fill pattern's advanced features?

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        Kevin1-Visitor
        1-Visitor
        Oct 16, 2016 2:34 AM UTC

        ‌I took a look at this but based on what I'm seeing although it will get points on the spheres surface it can't duplicate the method used to create the points. The most appropriate would be to pattern the points on a sketched curve but the projections or mappings of the points to the surface are off. From what I can see the pattern options can't handle the radial projection of the individual points which is required to get the points in the right places.

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        bnielsen-21-Visitor
        1-Visitor
        Oct 20, 2016 4:18 PM UTC

        Hi @BH001,

        It looks like you've gotten a lot of responses already, but I thought I'd add my $0.02:

        After skimming through the various responses, I saw that someone did effectively answer [correctly]: it's not possible to distribute N points on a sphere with perfectly even spacing between adjacent points when N is above a certain number (I'm not certain, but I seem to remember number N=20 for some reason.  I wouldn't swear to this though).

        However, this is an active problem in mathematics; please refer to this PDF of a relatively rigorous analysis of the problem: https://perswww.kuleuven.be/~u0017946/publications/Papers97/art97a-Saff-Kuijlaars-MI/Saff-Kuijlaars-MathIntel97.pdf

        Also, I didn't see it in that PDF but I distinctly remember reading about fibonacci arrangements of pollen as well, something that was studied in the first half of the 20th century by a well-known biologist (whose name also escapes me, of course).  I think this is the relevant paper: https://arxiv.org/pdf/0912.4540.pdf

        Also, these links may be of some help as well:

        http://stackoverflow.com/questions/9600801/evenly-distributing-n-points-on-a-sphere

        https://my.vanderbilt.edu/edsaff/spheres-manifolds/

        Please let us know how your research goes and what you decide on doing!

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          BHOoi
          BHOoi16-PearlAuthor
          16-Pearl
          Oct 21, 2016 1:14 AM UTC

          Thanks for those links, Ben. I will spend some time going through them but I doubt i will be able to understand them all .

          So far, the best solution is still through icosahedron but it has limited number of points and further splitting is pretty a tedious task.

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          TomD.inPDX17-Peridot
          17-Peridot
          Oct 21, 2016 1:46 AM UTC

          Something to consider is building 1 quadrant and learn how to use the transformation matrix.  When I was doing the Golf Ball, everything could be mirrored X and Y, then transform the set of 4, twice.

          The subdivision is the one thing that there has to be a better way.  You do know you can use polar coordinate systems, right?

          Is there an advantage there?

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